A spectral bound for vertex-transitive graphs and their spanning subgraphs
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For any finite, undirected, non-bipartite, vertex-transitive graph, we establish an explicit lower bound for the smallest eigenvalue of its normalised adjacency operator, which depends on the graph only through its degree and its vertex-Cheeger constant. We also prove an analogous result for a large class of irregular graphs, obtained as spanning subgraphs of vertex-transitive graphs. Using a result of Babai, we obtain a lower bound for the smallest eigenvalue of the normalised adjacency operator of a vertex-transitive graph in terms of its diameter and its degree.
Original language | English |
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Journal | Algebraic Combinatorics |
Volume | 6 |
Issue number | 3 |
Pages (from-to) | 689-706 |
Number of pages | 18 |
ISSN | 2589-5486 |
DOIs | |
Publication status | Published - 2023 |
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© 2023 Historia Actual Online.
- diameter, discrete Cheeger-Buser inequality, Spectral gap, vertex-transitive graphs
Research areas
ID: 382500709